A Mac Mini will serve you nicely. However, I wouldn't completely toss out the keyboard and mouse.... or the monitor. At the very least keep them around even if not connected. You CAN run headless but having a head and appendages can be quite helpful.
A NAS can be used as a Roon server but the BIG disadvantage is its anemic CPU if you plan to experiment with heavy duty DSP operations within Roon. Even the entry level Roon Nucleus can't handle all the DSP that Roon software is capable of but even the most entry level Mac Mini (like my M1) can handle it all.
I use my iPad with Roon Remote -or- I'll use the wireless bluetooth keyboard and mouse paired to Mini when displaying the Mini screen to the big 75" TV. I can control Roon this way or watch YouTube.
Roon is extremely flexible and there are multiple ways to run Roon server and to control it. There is no right way.
Here's a thought but it's just a thought.
If you place all of your music on an external SSD attached to your Mac it makes it super easy to move your music to another platform should you choose to. For example, I have the entry Mac Mini M1 and should I decide to buy a Mac Mini M4 I can simply relocate the SSD to it. And enable Roon Server software on the M4 Mini.
As for replacing your battery in the MacBook Pro I did that a few years ago on my older 13" MacBook Pro. There are several aftermarket batteries on Amazon. You just have to be careful to order one that will match your MacBook Pro's model designation. You'll find several video tutorials on OWC Mac Sales and YouTube.
